Outlier rejection for the weighted-mean KCRV

We propose new criteria to help select a subset of peer results for determining a weighted-mean Key Comparison Reference Value (KCRV) for describing Key Comparisons supporting the CIPM Mutual Recognition Arrangement (MRA). Often the results are all well behaved: their scatter is in the range expected from the Gaussian probability distributions associated with their stated standard uncertainties. In this case, the KCRV would usually be the inverse-variance weighted mean of all eligible results, the maximum likelihood estimate of independent Gaussian probability distributions. If most-but not all-of the results are well behaved, the comparison may be better described in terms of a KCRV computed with 'outliers' excluded from the weighted mean. An outlier's effects are quantified in terms of the logarithmic slope and logarithmic curvature of its associated probability density function in the vicinity of the consensus value. The outer tails of the probability distributions are generally not known with confidence, so two new criteria are suggested to help justify the identification of outliers: one based on uncertainty in the logarithmic slope, and the other based on uncertainty about whether the logarithmic curvature is negative definite.